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+# define COMPILER_VERSION_MINOR DEC(_COMPILER_VERSION/10 % 10)
+# define COMPILER_VERSION_PATCH DEC(_COMPILER_VERSION % 10)
+# endif
+
+
+/* These compilers are either not known or too old to define an
+ identification macro. Try to identify the platform and guess that
+ it is the native compiler. */
+#elif defined(__sgi)
+# define COMPILER_ID "MIPSpro"
+
+#elif defined(__hpux) || defined(__hpua)
+# define COMPILER_ID "HP"
+
+#else /* unknown compiler */
+# define COMPILER_ID ""
+#endif
+
+/* Construct the string literal in pieces to prevent the source from
+ getting matched. Store it in a pointer rather than an array
+ because some compilers will just produce instructions to fill the
+ array rather than assigning a pointer to a static array. */
+char const* info_compiler = "INFO" ":" "compiler[" COMPILER_ID "]";
+#ifdef SIMULATE_ID
+char const* info_simulate = "INFO" ":" "simulate[" SIMULATE_ID "]";
+#endif
+
+#ifdef __QNXNTO__
+char const* qnxnto = "INFO" ":" "qnxnto[]";
+#endif
+
+#if defined(__CRAYXE) || defined(__CRAYXC)
+char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]";
+#endif
+
+#define STRINGIFY_HELPER(X) #X
+#define STRINGIFY(X) STRINGIFY_HELPER(X)
+
+/* Identify known platforms by name. */
+#if defined(__linux) || defined(__linux__) || defined(linux)
+# define PLATFORM_ID "Linux"
+
+#elif defined(__CYGWIN__)
+# define PLATFORM_ID "Cygwin"
+
+#elif defined(__MINGW32__)
+# define PLATFORM_ID "MinGW"
+
+#elif defined(__APPLE__)
+# define PLATFORM_ID "Darwin"
+
+#elif defined(_WIN32) || defined(__WIN32__) || defined(WIN32)
+# define PLATFORM_ID "Windows"
+
+#elif defined(__FreeBSD__) || defined(__FreeBSD)
+# define PLATFORM_ID "FreeBSD"
+
+#elif defined(__NetBSD__) || defined(__NetBSD)
+# define PLATFORM_ID "NetBSD"
+
+#elif defined(__OpenBSD__) || defined(__OPENBSD)
+# define PLATFORM_ID "OpenBSD"
+
+#elif defined(__sun) || defined(sun)
+# define PLATFORM_ID "SunOS"
+
+#elif defined(_AIX) || defined(__AIX) || defined(__AIX__) || defined(__aix) || defined(__aix__)
+# define PLATFORM_ID "AIX"
+
+#elif defined(__sgi) || defined(__sgi__) || defined(_SGI)
+# define PLATFORM_ID "IRIX"
+
+#elif defined(__hpux) || defined(__hpux__)
+# define PLATFORM_ID "HP-UX"
+
+#elif defined(__HAIKU__)
+# define PLATFORM_ID "Haiku"
+
+#elif defined(__BeOS) || defined(__BEOS__) || defined(_BEOS)
+# define PLATFORM_ID "BeOS"
+
+#elif defined(__QNX__) || defined(__QNXNTO__)
+# define PLATFORM_ID "QNX"
+
+#elif defined(__tru64) || defined(_tru64) || defined(__TRU64__)
+# define PLATFORM_ID "Tru64"
+
+#elif defined(__riscos) || defined(__riscos__)
+# define PLATFORM_ID "RISCos"
+
+#elif defined(__sinix) || defined(__sinix__) || defined(__SINIX__)
+# define PLATFORM_ID "SINIX"
+
+#elif defined(__UNIX_SV__)
+# define PLATFORM_ID "UNIX_SV"
+
+#elif defined(__bsdos__)
+# define PLATFORM_ID "BSDOS"
+
+#elif defined(_MPRAS) || defined(MPRAS)
+# define PLATFORM_ID "MP-RAS"
+
+#elif defined(__osf) || defined(__osf__)
+# define PLATFORM_ID "OSF1"
+
+#elif defined(_SCO_SV) || defined(SCO_SV) || defined(sco_sv)
+# define PLATFORM_ID "SCO_SV"
+
+#elif defined(__ultrix) || defined(__ultrix__) || defined(_ULTRIX)
+# define PLATFORM_ID "ULTRIX"
+
+#elif defined(__XENIX__) || defined(_XENIX) || defined(XENIX)
+# define PLATFORM_ID "Xenix"
+
+#elif defined(__WATCOMC__)
+# if defined(__LINUX__)
+# define PLATFORM_ID "Linux"
+
+# elif defined(__DOS__)
+# define PLATFORM_ID "DOS"
+
+# elif defined(__OS2__)
+# define PLATFORM_ID "OS2"
+
+# elif defined(__WINDOWS__)
+# define PLATFORM_ID "Windows3x"
+
+# else /* unknown platform */
+# define PLATFORM_ID
+# endif
+
+#else /* unknown platform */
+# define PLATFORM_ID
+
+#endif
+
+/* For windows compilers MSVC and Intel we can determine
+ the architecture of the compiler being used. This is because
+ the compilers do not have flags that can change the architecture,
+ but rather depend on which compiler is being used
+*/
+#if defined(_WIN32) && defined(_MSC_VER)
+# if defined(_M_IA64)
+# define ARCHITECTURE_ID "IA64"
+
+# elif defined(_M_X64) || defined(_M_AMD64)
+# define ARCHITECTURE_ID "x64"
+
+# elif defined(_M_IX86)
+# define ARCHITECTURE_ID "X86"
+
+# elif defined(_M_ARM64)
+# define ARCHITECTURE_ID "ARM64"
+
+# elif defined(_M_ARM)
+# if _M_ARM == 4
+# define ARCHITECTURE_ID "ARMV4I"
+# elif _M_ARM == 5
+# define ARCHITECTURE_ID "ARMV5I"
+# else
+# define ARCHITECTURE_ID "ARMV" STRINGIFY(_M_ARM)
+# endif
+
+# elif defined(_M_MIPS)
+# define ARCHITECTURE_ID "MIPS"
+
+# elif defined(_M_SH)
+# define ARCHITECTURE_ID "SHx"
+
+# else /* unknown architecture */
+# define ARCHITECTURE_ID ""
+# endif
+
+#elif defined(__WATCOMC__)
+# if defined(_M_I86)
+# define ARCHITECTURE_ID "I86"
+
+# elif defined(_M_IX86)
+# define ARCHITECTURE_ID "X86"
+
+# else /* unknown architecture */
+# define ARCHITECTURE_ID ""
+# endif
+
+#elif defined(__IAR_SYSTEMS_ICC__) || defined(__IAR_SYSTEMS_ICC)
+# if defined(__ICCARM__)
+# define ARCHITECTURE_ID "ARM"
+
+# elif defined(__ICCAVR__)
+# define ARCHITECTURE_ID "AVR"
+
+# else /* unknown architecture */
+# define ARCHITECTURE_ID ""
+# endif
+#else
+# define ARCHITECTURE_ID
+#endif
+
+/* Convert integer to decimal digit literals. */
+#define DEC(n) \
+ ('0' + (((n) / 10000000)%10)), \
+ ('0' + (((n) / 1000000)%10)), \
+ ('0' + (((n) / 100000)%10)), \
+ ('0' + (((n) / 10000)%10)), \
+ ('0' + (((n) / 1000)%10)), \
+ ('0' + (((n) / 100)%10)), \
+ ('0' + (((n) / 10)%10)), \
+ ('0' + ((n) % 10))
+
+/* Convert integer to hex digit literals. */
+#define HEX(n) \
+ ('0' + ((n)>>28 & 0xF)), \
+ ('0' + ((n)>>24 & 0xF)), \
+ ('0' + ((n)>>20 & 0xF)), \
+ ('0' + ((n)>>16 & 0xF)), \
+ ('0' + ((n)>>12 & 0xF)), \
+ ('0' + ((n)>>8 & 0xF)), \
+ ('0' + ((n)>>4 & 0xF)), \
+ ('0' + ((n) & 0xF))
+
+/* Construct a string literal encoding the version number components. */
+#ifdef COMPILER_VERSION_MAJOR
+char const info_version[] = {
+ 'I', 'N', 'F', 'O', ':',
+ 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','[',
+ COMPILER_VERSION_MAJOR,
+# ifdef COMPILER_VERSION_MINOR
+ '.', COMPILER_VERSION_MINOR,
+# ifdef COMPILER_VERSION_PATCH
+ '.', COMPILER_VERSION_PATCH,
+# ifdef COMPILER_VERSION_TWEAK
+ '.', COMPILER_VERSION_TWEAK,
+# endif
+# endif
+# endif
+ ']','\0'};
+#endif
+
+/* Construct a string literal encoding the internal version number. */
+#ifdef COMPILER_VERSION_INTERNAL
+char const info_version_internal[] = {
+ 'I', 'N', 'F', 'O', ':',
+ 'c','o','m','p','i','l','e','r','_','v','e','r','s','i','o','n','_',
+ 'i','n','t','e','r','n','a','l','[',
+ COMPILER_VERSION_INTERNAL,']','\0'};
+#endif
+
+/* Construct a string literal encoding the version number components. */
+#ifdef SIMULATE_VERSION_MAJOR
+char const info_simulate_version[] = {
+ 'I', 'N', 'F', 'O', ':',
+ 's','i','m','u','l','a','t','e','_','v','e','r','s','i','o','n','[',
+ SIMULATE_VERSION_MAJOR,
+# ifdef SIMULATE_VERSION_MINOR
+ '.', SIMULATE_VERSION_MINOR,
+# ifdef SIMULATE_VERSION_PATCH
+ '.', SIMULATE_VERSION_PATCH,
+# ifdef SIMULATE_VERSION_TWEAK
+ '.', SIMULATE_VERSION_TWEAK,
+# endif
+# endif
+# endif
+ ']','\0'};
+#endif
+
+/* Construct the string literal in pieces to prevent the source from
+ getting matched. Store it in a pointer rather than an array
+ because some compilers will just produce instructions to fill the
+ array rather than assigning a pointer to a static array. */
+char const* info_platform = "INFO" ":" "platform[" PLATFORM_ID "]";
+char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]";
+
+
+
+
+#if !defined(__STDC__)
+# if (defined(_MSC_VER) && !defined(__clang__)) \
+ || (defined(__ibmxl__) || defined(__IBMC__))
+# define C_DIALECT "90"
+# else
+# define C_DIALECT
+# endif
+#elif __STDC_VERSION__ >= 201000L
+# define C_DIALECT "11"
+#elif __STDC_VERSION__ >= 199901L
+# define C_DIALECT "99"
+#else
+# define C_DIALECT "90"
+#endif
+const char* info_language_dialect_default =
+ "INFO" ":" "dialect_default[" C_DIALECT "]";
+
+/*--------------------------------------------------------------------------*/
+
+#ifdef ID_VOID_MAIN
+void main() {}
+#else
+# if defined(__CLASSIC_C__)
+int main(argc, argv) int argc; char *argv[];
+# else
+int main(int argc, char* argv[])
+# endif
+{
+ int require = 0;
+ require += info_compiler[argc];
+ require += info_platform[argc];
+ require += info_arch[argc];
+#ifdef COMPILER_VERSION_MAJOR
+ require += info_version[argc];
+#endif
+#ifdef COMPILER_VERSION_INTERNAL
+ require += info_version_internal[argc];
+#endif
+#ifdef SIMULATE_ID
+ require += info_simulate[argc];
+#endif
+#ifdef SIMULATE_VERSION_MAJOR
+ require += info_simulate_version[argc];
+#endif
+#if defined(__CRAYXE) || defined(__CRAYXC)
+ require += info_cray[argc];
+#endif
+ require += info_language_dialect_default[argc];
+ (void)argv;
+ return require;
+}
+#endif
diff --git a/sgi2018/CMakeFiles/3.13.4/CompilerIdCXX/CMakeCXXCompilerId.cpp b/sgi2018/CMakeFiles/3.13.4/CompilerIdCXX/CMakeCXXCompilerId.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..b728b6329139a9ff24adbe3b6e270e5bfcc3a426
--- /dev/null
+++ b/sgi2018/CMakeFiles/3.13.4/CompilerIdCXX/CMakeCXXCompilerId.cpp
@@ -0,0 +1,602 @@
+/* This source file must have a .cpp extension so that all C++ compilers
+ recognize the extension without flags. Borland does not know .cxx for
+ example. */
+#ifndef __cplusplus
+# error "A C compiler has been selected for C++."
+#endif
+
+
+/* Version number components: V=Version, R=Revision, P=Patch
+ Version date components: YYYY=Year, MM=Month, DD=Day */
+
+#if defined(__COMO__)
+# define COMPILER_ID "Comeau"
+ /* __COMO_VERSION__ = VRR */
+# define COMPILER_VERSION_MAJOR DEC(__COMO_VERSION__ / 100)
+# define COMPILER_VERSION_MINOR DEC(__COMO_VERSION__ % 100)
+
+#elif defined(__INTEL_COMPILER) || defined(__ICC)
+# define COMPILER_ID "Intel"
+# if defined(_MSC_VER)
+# define SIMULATE_ID "MSVC"
+# endif
+ /* __INTEL_COMPILER = VRP */
+# define COMPILER_VERSION_MAJOR DEC(__INTEL_COMPILER/100)
+# define COMPILER_VERSION_MINOR DEC(__INTEL_COMPILER/10 % 10)
+# if defined(__INTEL_COMPILER_UPDATE)
+# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER_UPDATE)
+# else
+# define COMPILER_VERSION_PATCH DEC(__INTEL_COMPILER % 10)
+# endif
+# if defined(__INTEL_COMPILER_BUILD_DATE)
+ /* __INTEL_COMPILER_BUILD_DATE = YYYYMMDD */
+# define COMPILER_VERSION_TWEAK DEC(__INTEL_COMPILER_BUILD_DATE)
+# endif
+# if defined(_MSC_VER)
+ /* _MSC_VER = VVRR */
+# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100)
+# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100)
+# endif
+
+#elif defined(__PATHCC__)
+# define COMPILER_ID "PathScale"
+# define COMPILER_VERSION_MAJOR DEC(__PATHCC__)
+# define COMPILER_VERSION_MINOR DEC(__PATHCC_MINOR__)
+# if defined(__PATHCC_PATCHLEVEL__)
+# define COMPILER_VERSION_PATCH DEC(__PATHCC_PATCHLEVEL__)
+# endif
+
+#elif defined(__BORLANDC__) && defined(__CODEGEARC_VERSION__)
+# define COMPILER_ID "Embarcadero"
+# define COMPILER_VERSION_MAJOR HEX(__CODEGEARC_VERSION__>>24 & 0x00FF)
+# define COMPILER_VERSION_MINOR HEX(__CODEGEARC_VERSION__>>16 & 0x00FF)
+# define COMPILER_VERSION_PATCH DEC(__CODEGEARC_VERSION__ & 0xFFFF)
+
+#elif defined(__BORLANDC__)
+# define COMPILER_ID "Borland"
+ /* __BORLANDC__ = 0xVRR */
+# define COMPILER_VERSION_MAJOR HEX(__BORLANDC__>>8)
+# define COMPILER_VERSION_MINOR HEX(__BORLANDC__ & 0xFF)
+
+#elif defined(__WATCOMC__) && __WATCOMC__ < 1200
+# define COMPILER_ID "Watcom"
+ /* __WATCOMC__ = VVRR */
+# define COMPILER_VERSION_MAJOR DEC(__WATCOMC__ / 100)
+# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10)
+# if (__WATCOMC__ % 10) > 0
+# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10)
+# endif
+
+#elif defined(__WATCOMC__)
+# define COMPILER_ID "OpenWatcom"
+ /* __WATCOMC__ = VVRP + 1100 */
+# define COMPILER_VERSION_MAJOR DEC((__WATCOMC__ - 1100) / 100)
+# define COMPILER_VERSION_MINOR DEC((__WATCOMC__ / 10) % 10)
+# if (__WATCOMC__ % 10) > 0
+# define COMPILER_VERSION_PATCH DEC(__WATCOMC__ % 10)
+# endif
+
+#elif defined(__SUNPRO_CC)
+# define COMPILER_ID "SunPro"
+# if __SUNPRO_CC >= 0x5100
+ /* __SUNPRO_CC = 0xVRRP */
+# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_CC>>12)
+# define COMPILER_VERSION_MINOR HEX(__SUNPRO_CC>>4 & 0xFF)
+# define COMPILER_VERSION_PATCH HEX(__SUNPRO_CC & 0xF)
+# else
+ /* __SUNPRO_CC = 0xVRP */
+# define COMPILER_VERSION_MAJOR HEX(__SUNPRO_CC>>8)
+# define COMPILER_VERSION_MINOR HEX(__SUNPRO_CC>>4 & 0xF)
+# define COMPILER_VERSION_PATCH HEX(__SUNPRO_CC & 0xF)
+# endif
+
+#elif defined(__HP_aCC)
+# define COMPILER_ID "HP"
+ /* __HP_aCC = VVRRPP */
+# define COMPILER_VERSION_MAJOR DEC(__HP_aCC/10000)
+# define COMPILER_VERSION_MINOR DEC(__HP_aCC/100 % 100)
+# define COMPILER_VERSION_PATCH DEC(__HP_aCC % 100)
+
+#elif defined(__DECCXX)
+# define COMPILER_ID "Compaq"
+ /* __DECCXX_VER = VVRRTPPPP */
+# define COMPILER_VERSION_MAJOR DEC(__DECCXX_VER/10000000)
+# define COMPILER_VERSION_MINOR DEC(__DECCXX_VER/100000 % 100)
+# define COMPILER_VERSION_PATCH DEC(__DECCXX_VER % 10000)
+
+#elif defined(__IBMCPP__) && defined(__COMPILER_VER__)
+# define COMPILER_ID "zOS"
+# if defined(__ibmxl__)
+# define COMPILER_VERSION_MAJOR DEC(__ibmxl_version__)
+# define COMPILER_VERSION_MINOR DEC(__ibmxl_release__)
+# define COMPILER_VERSION_PATCH DEC(__ibmxl_modification__)
+# define COMPILER_VERSION_TWEAK DEC(__ibmxl_ptf_fix_level__)
+# else
+ /* __IBMCPP__ = VRP */
+# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100)
+# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10)
+# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10)
+# endif
+
+
+#elif defined(__ibmxl__) || (defined(__IBMCPP__) && !defined(__COMPILER_VER__) && __IBMCPP__ >= 800)
+# define COMPILER_ID "XL"
+# if defined(__ibmxl__)
+# define COMPILER_VERSION_MAJOR DEC(__ibmxl_version__)
+# define COMPILER_VERSION_MINOR DEC(__ibmxl_release__)
+# define COMPILER_VERSION_PATCH DEC(__ibmxl_modification__)
+# define COMPILER_VERSION_TWEAK DEC(__ibmxl_ptf_fix_level__)
+# else
+ /* __IBMCPP__ = VRP */
+# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100)
+# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10)
+# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10)
+# endif
+
+
+#elif defined(__IBMCPP__) && !defined(__COMPILER_VER__) && __IBMCPP__ < 800
+# define COMPILER_ID "VisualAge"
+# if defined(__ibmxl__)
+# define COMPILER_VERSION_MAJOR DEC(__ibmxl_version__)
+# define COMPILER_VERSION_MINOR DEC(__ibmxl_release__)
+# define COMPILER_VERSION_PATCH DEC(__ibmxl_modification__)
+# define COMPILER_VERSION_TWEAK DEC(__ibmxl_ptf_fix_level__)
+# else
+ /* __IBMCPP__ = VRP */
+# define COMPILER_VERSION_MAJOR DEC(__IBMCPP__/100)
+# define COMPILER_VERSION_MINOR DEC(__IBMCPP__/10 % 10)
+# define COMPILER_VERSION_PATCH DEC(__IBMCPP__ % 10)
+# endif
+
+
+#elif defined(__PGI)
+# define COMPILER_ID "PGI"
+# define COMPILER_VERSION_MAJOR DEC(__PGIC__)
+# define COMPILER_VERSION_MINOR DEC(__PGIC_MINOR__)
+# if defined(__PGIC_PATCHLEVEL__)
+# define COMPILER_VERSION_PATCH DEC(__PGIC_PATCHLEVEL__)
+# endif
+
+#elif defined(_CRAYC)
+# define COMPILER_ID "Cray"
+# define COMPILER_VERSION_MAJOR DEC(_RELEASE_MAJOR)
+# define COMPILER_VERSION_MINOR DEC(_RELEASE_MINOR)
+
+#elif defined(__TI_COMPILER_VERSION__)
+# define COMPILER_ID "TI"
+ /* __TI_COMPILER_VERSION__ = VVVRRRPPP */
+# define COMPILER_VERSION_MAJOR DEC(__TI_COMPILER_VERSION__/1000000)
+# define COMPILER_VERSION_MINOR DEC(__TI_COMPILER_VERSION__/1000 % 1000)
+# define COMPILER_VERSION_PATCH DEC(__TI_COMPILER_VERSION__ % 1000)
+
+#elif defined(__FUJITSU) || defined(__FCC_VERSION) || defined(__fcc_version)
+# define COMPILER_ID "Fujitsu"
+
+#elif defined(__SCO_VERSION__)
+# define COMPILER_ID "SCO"
+
+#elif defined(__clang__) && defined(__apple_build_version__)
+# define COMPILER_ID "AppleClang"
+# if defined(_MSC_VER)
+# define SIMULATE_ID "MSVC"
+# endif
+# define COMPILER_VERSION_MAJOR DEC(__clang_major__)
+# define COMPILER_VERSION_MINOR DEC(__clang_minor__)
+# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__)
+# if defined(_MSC_VER)
+ /* _MSC_VER = VVRR */
+# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100)
+# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100)
+# endif
+# define COMPILER_VERSION_TWEAK DEC(__apple_build_version__)
+
+#elif defined(__clang__)
+# define COMPILER_ID "Clang"
+# if defined(_MSC_VER)
+# define SIMULATE_ID "MSVC"
+# endif
+# define COMPILER_VERSION_MAJOR DEC(__clang_major__)
+# define COMPILER_VERSION_MINOR DEC(__clang_minor__)
+# define COMPILER_VERSION_PATCH DEC(__clang_patchlevel__)
+# if defined(_MSC_VER)
+ /* _MSC_VER = VVRR */
+# define SIMULATE_VERSION_MAJOR DEC(_MSC_VER / 100)
+# define SIMULATE_VERSION_MINOR DEC(_MSC_VER % 100)
+# endif
+
+#elif defined(__GNUC__) || defined(__GNUG__)
+# define COMPILER_ID "GNU"
+# if defined(__GNUC__)
+# define COMPILER_VERSION_MAJOR DEC(__GNUC__)
+# else
+# define COMPILER_VERSION_MAJOR DEC(__GNUG__)
+# endif
+# if defined(__GNUC_MINOR__)
+# define COMPILER_VERSION_MINOR DEC(__GNUC_MINOR__)
+# endif
+# if defined(__GNUC_PATCHLEVEL__)
+# define COMPILER_VERSION_PATCH DEC(__GNUC_PATCHLEVEL__)
+# endif
+
+#elif defined(_MSC_VER)
+# define COMPILER_ID "MSVC"
+ /* _MSC_VER = VVRR */
+# define COMPILER_VERSION_MAJOR DEC(_MSC_VER / 100)
+# define COMPILER_VERSION_MINOR DEC(_MSC_VER % 100)
+# if defined(_MSC_FULL_VER)
+# if _MSC_VER >= 1400
+ /* _MSC_FULL_VER = VVRRPPPPP */
+# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 100000)
+# else
+ /* _MSC_FULL_VER = VVRRPPPP */
+# define COMPILER_VERSION_PATCH DEC(_MSC_FULL_VER % 10000)
+# endif
+# endif
+# if defined(_MSC_BUILD)
+# define COMPILER_VERSION_TWEAK DEC(_MSC_BUILD)
+# endif
+
+#elif defined(__VISUALDSPVERSION__) || defined(__ADSPBLACKFIN__) || defined(__ADSPTS__) || defined(__ADSP21000__)
+# define COMPILER_ID "ADSP"
+#if defined(__VISUALDSPVERSION__)
+ /* __VISUALDSPVERSION__ = 0xVVRRPP00 */
+# define COMPILER_VERSION_MAJOR HEX(__VISUALDSPVERSION__>>24)
+# define COMPILER_VERSION_MINOR HEX(__VISUALDSPVERSION__>>16 & 0xFF)
+# define COMPILER_VERSION_PATCH HEX(__VISUALDSPVERSION__>>8 & 0xFF)
+#endif
+
+#elif defined(__IAR_SYSTEMS_ICC__) || defined(__IAR_SYSTEMS_ICC)
+# define COMPILER_ID "IAR"
+# if defined(__VER__)
+# define COMPILER_VERSION_MAJOR DEC((__VER__) / 1000000)
+# define COMPILER_VERSION_MINOR DEC(((__VER__) / 1000) % 1000)
+# define COMPILER_VERSION_PATCH DEC((__VER__) % 1000)
+# define COMPILER_VERSION_INTERNAL DEC(__IAR_SYSTEMS_ICC__)
+# endif
+
+#elif defined(__ARMCC_VERSION)
+# define COMPILER_ID "ARMCC"
+#if __ARMCC_VERSION >= 1000000
+ /* __ARMCC_VERSION = VRRPPPP */
+ # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/1000000)
+ # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 100)
+ # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000)
+#else
+ /* __ARMCC_VERSION = VRPPPP */
+ # define COMPILER_VERSION_MAJOR DEC(__ARMCC_VERSION/100000)
+ # define COMPILER_VERSION_MINOR DEC(__ARMCC_VERSION/10000 % 10)
+ # define COMPILER_VERSION_PATCH DEC(__ARMCC_VERSION % 10000)
+#endif
+
+
+#elif defined(_SGI_COMPILER_VERSION) || defined(_COMPILER_VERSION)
+# define COMPILER_ID "MIPSpro"
+# if defined(_SGI_COMPILER_VERSION)
+ /* _SGI_COMPILER_VERSION = VRP */
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+# define COMPILER_VERSION_PATCH DEC(_SGI_COMPILER_VERSION % 10)
+# else
+ /* _COMPILER_VERSION = VRP */
+# define COMPILER_VERSION_MAJOR DEC(_COMPILER_VERSION/100)
+# define COMPILER_VERSION_MINOR DEC(_COMPILER_VERSION/10 % 10)
+# define COMPILER_VERSION_PATCH DEC(_COMPILER_VERSION % 10)
+# endif
+
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+ identification macro. Try to identify the platform and guess that
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+#define STRINGIFY(X) STRINGIFY_HELPER(X)
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+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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+ 8. Limitation of Liability. In no event and under no legal theory,
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+ END OF TERMS AND CONDITIONS
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+ Copyright 2019 Nestor Demeure
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+ Licensed under the Apache License, Version 2.0 (the "License");
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+ See the License for the specific language governing permissions and
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index 0000000000000000000000000000000000000000..f794b2e04ecb605d80af86fa48f7d1e69562ffd9
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diff --git a/sgi2018/plot.R b/sgi2018/plot.R
new file mode 100644
index 0000000000000000000000000000000000000000..042f29087b6de0ee933f64e0a1e5739c093ec86f
--- /dev/null
+++ b/sgi2018/plot.R
@@ -0,0 +1,60 @@
+
+library(dplyr)
+library(ggplot2)
+
+#--------------------------------------------------------------------------------------------------
+# IMPORT DATA
+
+folder <- "output"
+pathEigenvalues <- paste(folder, "phase_eigenvalues.csv", sep='/')
+pathMontecarlo <- paste(folder, "phase_montecarlo.csv", sep='/')
+pathXi <- paste(folder, "xi.csv", sep='/')
+
+eigenvalues <- data.table::fread(pathEigenvalues)
+montecarlo <- data.table::fread(pathMontecarlo)
+
+xi <- data.table::fread(pathXi)
+xi <- complex(real = xi$V1, imaginary = xi$V2)
+
+#--------------------------------------------------------------------------------------------------
+# ALPHA
+
+# alpha used to reflect distance to xi=0
+alpha <- 1 / (1 + Mod(xi))
+minalpha <- 0.2
+alpha <- ifelse(alpha > minalpha, alpha, minalpha)
+
+#--------------------------------------------------------------------------------------------------
+# PLOT DATA
+
+# model that will be plotted
+model <- montecarlo
+
+# plot axis
+plot <- ggplot() +
+ theme_light() +
+ labs(x = "θ · ð•½[λ]^½", y="1 / ð•´[λ]^½") +
+ coord_cartesian(xlim = c(353.5, 361.5), ylim = c(2.825e-5, 2.875e-5))
+
+# plots eigenvalues in the background
+for(i in 1:(ncol(eigenvalues)/2))
+{
+ j <- 2*i - 1
+ data <- eigenvalues[,j:(j+1)]
+ colnames(data) <- c("x", "y")
+ plot <- plot + geom_point(data=data, aes(x=x, y=y), colour = 'black', alpha=alpha, size = alpha)
+}
+
+# plot tracked eigenvalues
+nbTarget <- ncol(model)/2
+model_colors <- rainbow(nbTarget)
+for(i in 1:nbTarget)
+{
+ j <- 2*i - 1
+ data <- model[,j:(j+1)]
+ colnames(data) <- c("x", "y")
+ plot <- plot + geom_point(data=data, aes(x=x, y=y), colour = model_colors[i], alpha=alpha, size = 0.5 + alpha)
+}
+
+X11()
+print(plot)
diff --git a/sgi2018/readme.md b/sgi2018/readme.md
new file mode 100644
index 0000000000000000000000000000000000000000..7df4c1feca3631e151e7e2bfb75e252e2daac782
--- /dev/null
+++ b/sgi2018/readme.md
@@ -0,0 +1,52 @@
+# Eigen follower
+
+## Description
+
+There exists several methods to simulate numerically sound propagation in an inhomogeneous medium.
+The method we are going to use here is called *normal modes decomposition*.
+
+The idea is to use the eigenfunctions and eigenvalues of the operator ![f1] which characterize the different waveguides.
+The signal will be the sum of different wavepackets each one propagating in the different waveguides.
+Thus, the key point is to determine the spectrum of ![f2] in order to compute the different contributions to the propagated signal.
+Numerically, the operator is discretized in a matrix whose spectrum can be computed with classical methods.
+
+The aim of this study is to see how the spectrum behaves when the medium is perturbed.
+We will described the perturbation using a random parameter ξ (gaussian vector of dimension 2) and thereby the matrix will be seen as a function of ξ.
+We want to see how the eigenvalues of a matrix reacts to this perturbation first with a Monte-Carlo approach and then using Polynomial Chaos expansion.
+
+This project contains the code to generate different realizations of the matrix, compute their spectrum and link the different realizations of a given eigenvalue.
+It also contains the calibration of a chaos polynomials based metamodel to speed up computations.
+
+[f1]: http://chart.apis.google.com/chart?cht=tx&chl=\mathcal{L}\psi=\frac{d^2\psi}{dz^2}%2B\frac{\omega^2}{c(z)^2}\psi=\lambda\psi
+[f2]: http://chart.apis.google.com/chart?cht=tx&chl=\mathcal{L}
+
+## Usage
+
+The project is self contained, you just need [make](https://en.wikipedia.org/wiki/Make_(software)) and [cmake](https://cmake.org/) (which should already be installed on your computer) in order to compile.
+
+To compile, run `cmake .` followed with `make`.
+
+In order to plot the results, you can use and modify the `plot.R` script (you can run it with `Rscript plot.R`) which will output a pdf to the output folder.
+Note that you might need to install some R packages (`ggplot2`, `dplyr` and `data.table`) in order to get the `plot.R` script running.
+
+**Warning:** Do not forget to clone the project with its submodules (`git clone --recurse-submodules git@gitlab.com:nestordemeure/sgi2018.git`) or to update them (`git submodule update --init --recursive
+`) in order to download [Eigen](http://eigen.tuxfamily.org/index.php?title=Main_Page) with the rest of the project.
+If you decide to download Eigen separately, we recommend the [version 3.3](https://gitlab.com/kemen209/eigen/tree/branches/3.3).
+
+## Organisation of the files
+
+The `types` file contains all the types used in the project (one could change them here).
+
+The problem definition is in the `main` file.
+
+The `generator` file contains the code needed to generate the matrix whose eigenvalues are of interest.
+
+The `tools` folder contains function used in the project (such as writing to a csv and reproducing some of matlab's functions).
+
+The `follower` folder contains the code used to follow an eigenvalue when the matrix is changed (via a perturbation or a change in omega).
+
+## Credits
+
+The code was implemented by Nestor Demeure based on a Matlab implementation of chaos polynomials applied to this particular problem by Alexandre Goupy.
+
+
diff --git a/sgi2018/src/follower/follow.h b/sgi2018/src/follower/follow.h
new file mode 100644
index 0000000000000000000000000000000000000000..61f78448c81cc3595a89e346a35a9810dea0a11e
--- /dev/null
+++ b/sgi2018/src/follower/follow.h
@@ -0,0 +1,92 @@
+#pragma once
+
+#include <stack>
+#include "../types.h"
+#include "point.h"
+
+namespace Follow
+{
+ // goes from a point to another in a single step (as bad as it might be)
+ // given the index of a target in the first point, returns the index of the target in the last point
+ std::vector<unsigned int> instantStep(const Point& startPoint, const Point& endPoint, const std::vector<unsigned int>& indexTargets)
+ {
+ number distance; std::vector<unsigned int> indexes;
+ std::tie(indexes, distance) = endPoint.findClosest(endPoint, indexTargets);
+
+ return indexes;
+ }
+
+ // goes from a point to another with a fixed step size
+ // given the index of a target in the first point, returns the index of the target in the last point
+ std::vector<unsigned int> constantStep(const Point& startPoint, const Point& endPoint, const std::vector<unsigned int>& indexTargets,
+ const unsigned int maxStep = 100)
+ {
+ Point currentPoint = startPoint;
+ std::vector<unsigned int> currentIndexes = indexTargets;
+ number distance; // dummy variable, useless here
+
+ for(unsigned int step = 0; step <= maxStep; step++)
+ {
+ const Point nextPoint = Point::midPoint(startPoint, maxStep-step, endPoint, step);
+ std::tie(currentIndexes, distance) = nextPoint.findClosest(currentPoint, currentIndexes);
+ currentPoint = nextPoint;
+ }
+
+ return currentIndexes;
+ }
+
+ // goes from a point to another with an adaptiv stepsize (trying to keep the error under a threshold)
+ // given the index of a target in the first point, returns the index of the target in the last point
+ // one can define minstepsize, the minimum distance between two different points, in order to avoidhaving the search stuck in local discontinuities
+ // (sqrt(3) is the diagonal of a square in 3D)
+ std::vector<unsigned int> adaptativStep(const Point& startPoint, const Point& endPoint, const std::vector<unsigned int>& indexTargets,
+ const number distanceThreshold = 0.05, const number minstepsize = std::sqrt(3.)*1e-6)
+ {
+ Point currentPoint = startPoint;
+ std::vector<unsigned int> currentIndexes = indexTargets;
+
+ // information on potential relaxation of the threshold
+ number maxAcceptedDistance = distanceThreshold;
+ Point pointatMaxDistance;
+
+ std::stack<Point> nextPoints;
+ nextPoints.push(endPoint);
+ while(not nextPoints.empty())
+ {
+ const Point& nextPoint = nextPoints.top();
+
+ // tries to follow the target to the next point
+ number distance; std::vector<unsigned int> nextIndexes;
+ std::tie(nextIndexes, distance) = nextPoint.findClosest(currentPoint, currentIndexes);
+
+ if ((distance <= distanceThreshold) || (Point::distance(currentPoint, nextPoint) <= minstepsize))
+ {
+ // stores information our position if we had to relax the threshold
+ if (distance > maxAcceptedDistance)
+ {
+ maxAcceptedDistance = distance;
+ pointatMaxDistance = currentPoint;
+ }
+
+ // no need for a refinement, we accept the point
+ currentIndexes = nextIndexes;
+ currentPoint = nextPoint;
+ nextPoints.pop();
+ }
+ else
+ {
+ // the next step is too far away, we need to refine
+ const Point intermediatePoint = Point::midPoint(currentPoint, nextPoint);
+ nextPoints.push(intermediatePoint);
+ }
+ }
+
+ // display informations on the worst relaxation that had to happen
+ if (maxAcceptedDistance > distanceThreshold)
+ {
+ std::cerr << "We had to locally relax the threshold to " << maxAcceptedDistance << " around " << pointatMaxDistance << '.' << std::endl;
+ }
+
+ return currentIndexes;
+ }
+}
diff --git a/sgi2018/src/follower/point.h b/sgi2018/src/follower/point.h
new file mode 100644
index 0000000000000000000000000000000000000000..0400ea945632d7bc836686e486b285ca210749e9
--- /dev/null
+++ b/sgi2018/src/follower/point.h
@@ -0,0 +1,187 @@
+#pragma once
+
+#include <cmath>
+#include <limits>
+#include "../types.h"
+#include "../generator.h"
+
+//-------------------------------------------------------------------------------------------------
+// COSINE SIMILARITY
+
+// returns the cosine similarity between two normalised complex vectors
+number cosineSimilarity(const ComplexVector& v1, const ComplexVector& v2)
+{
+ return std::abs(v1.conjugate().dot(v2));
+}
+
+//-------------------------------------------------------------------------------------------------
+// STEP
+
+/*
+ * used to encapsulate a point
+ * contains omega, the noise, the eigenvectors and the formated eigenvalues (no need to keep the raw eigenvalues)
+ */
+class Point
+{
+public:
+ unsigned int size;
+ number omega;
+ complexNumber xi;
+ ComplexMatrix eigenVectors;
+ ComplexVector formatedEigenvalues;
+
+ // constructor that does nothing (usefull to init arrays)
+ Point(): size(0), omega(0), xi(0), eigenVectors(), formatedEigenvalues()
+ {}
+
+ // creates a new point at the given omega and xi
+ Point(const number omega, const unsigned int size, const complexNumber& xi = complexNumber(0.,0.)): size(size), omega(omega), xi(xi), eigenVectors(), formatedEigenvalues()
+ {
+ const complexNumber complexOmega = complexNumber(omega, 0.01);
+ const ComplexMatrix mat = generator(complexOmega, size, xi);
+ Eigen::ComplexEigenSolver<ComplexMatrix> solver(mat);
+ const ComplexVector& eigenValues = solver.eigenvalues();
+ eigenVectors = solver.eigenvectors();
+ formatedEigenvalues = eigenValues.unaryExpr([](complexNumber e){return transformEigenvalue(e) ;});
+ }
+
+ // returns the euclidian distance between two points
+ static number distance(const Point& point1, const Point& point2)
+ {
+ const number dOmega = point1.omega - point2.omega;
+ const complexNumber dxi = point1.xi - point2.xi;
+ return STD::sqrt(dOmega*dOmega + std::norm(dxi));
+ }
+
+ // returns the midpoint
+ static Point midPoint(const Point& point1, const Point& point2)
+ {
+ const number omega = (point1.omega + point2.omega) / number(2.);
+ const complexNumber xi = (point1.xi + point2.xi) / number(2.);
+ unsigned int size = point1.size;
+
+ return Point(omega, size, xi);
+ }
+
+ // returns the barycenter of two points
+ static Point midPoint(const Point& point1, const number& weight1, const Point& point2, const number weight2)
+ {
+ const number totalWeight = weight1 + weight2;
+ const number omega = (point1.omega*weight1 + point2.omega*weight2) / totalWeight;
+ const complexNumber xi = (point1.xi*weight1 + point2.xi*weight2) / totalWeight;
+ unsigned int size = point1.size;
+
+ return Point(omega, size, xi);
+ }
+
+ // given several eigenvectors, return the indexes of their closest eigenvectors in this point and the maximum distance to the target
+ // TODO this algorithm could be much faster with better datastructures
+ std::pair<std::vector<unsigned int>, number> findClosest(const Point& targetPoint, const std::vector<unsigned int>& indexTargets) const
+ {
+ std::vector<unsigned int> indexclosest(indexTargets.size());
+ number distance = 1.;
+
+ // builds similarity matrix
+ Matrix similarityMatrix(indexTargets.size(), eigenVectors.cols());
+ for (unsigned int r=0; r<indexTargets.size(); r++)
+ {
+ const ComplexVector& vector = targetPoint.eigenVectors.col(indexTargets[r]);
+ for (unsigned int c=0; c<eigenVectors.cols(); c++)
+ {
+ similarityMatrix(r,c) = cosineSimilarity(eigenVectors.col(c), vector);
+ }
+ }
+
+ // finds closest vectors
+ for (unsigned int v=0; v<indexTargets.size(); v++)
+ {
+ unsigned int bestr = 0;
+ unsigned int bestc = 0;
+ number bestSimilarity = 0.;
+
+ // finds best similarity in all of the matrix
+ for (unsigned int r=0; r < indexTargets.size(); r++)
+ {
+ for (unsigned int c=0; c < eigenVectors.cols(); c++)
+ {
+ const number similarity = similarityMatrix(r,c);
+ if ((similarity > bestSimilarity) and not STD::isnan(similarity))
+ {
+ bestr = r;
+ bestc = c;
+ bestSimilarity = similarity;
+ }
+ }
+ }
+
+ // stores best result so far
+ indexclosest[bestr] = bestc;
+ distance = 1. - bestSimilarity;
+ // make given row and column unatractiv for latter iterations
+ similarityMatrix.row(bestr).array() = -1.;
+ similarityMatrix.col(bestc).array() = -1.;
+ }
+
+ return std::make_pair(indexclosest, distance);
+ }
+
+ // given an eigenvalue, return the index of the closest eigenvalue in this point and its distance to the target
+ // TODO this algorithm could be much faster with better datastructures
+ std::pair<std::vector<unsigned int>, number> findClosest(const std::vector<complexNumber>& formatedTargetEigenValues) const
+ {
+ std::vector<unsigned int> indexclosest(formatedTargetEigenValues.size());
+ number finalDistance = 0.;
+
+ // builds similarity matrix
+ Matrix distanceMatrix(formatedTargetEigenValues.size(), eigenVectors.cols());
+ for (unsigned int r=0; r<formatedTargetEigenValues.size(); r++)
+ {
+ const complexNumber& formatedEigenvalue = formatedTargetEigenValues[r];
+ for (unsigned int c=0; c < eigenVectors.cols(); c++)
+ {
+ distanceMatrix(r,c) = std::abs(formatedEigenvalues[c] - formatedEigenvalue);
+ }
+ }
+
+ // finds closest vectors
+ for (unsigned int v=0; v<formatedTargetEigenValues.size(); v++)
+ {
+ unsigned int bestr = 0;
+ unsigned int bestc = 0;
+ number minDistance = std::numeric_limits<number>::infinity();
+
+ // finds best similarity in all of the matrix
+ for (unsigned int r=0; r<formatedTargetEigenValues.size(); r++)
+ {
+ for (unsigned int c=0; c<eigenVectors.cols(); c++)
+ {
+ const number distance = distanceMatrix(r,c);
+ if (distance < minDistance)
+ {
+ bestr = r;
+ bestc = c;
+ minDistance = distance;
+ }
+ }
+ }
+
+ // stores best result so far
+ indexclosest[bestr] = bestc;
+ finalDistance = minDistance;
+ // make given row and column unatractiv for latter iterations
+ distanceMatrix.row(bestr).array() = std::numeric_limits<number>::infinity();
+ distanceMatrix.col(bestc).array() = std::numeric_limits<number>::infinity();
+ }
+
+ return std::make_pair(indexclosest, finalDistance);
+ }
+};
+
+// streaming operator to properly display a point
+std::ostream& operator<< (std::ostream& stream, const Point& point)
+{
+ stream << "{omega: " << point.omega << " xi: " << point.xi << '}';
+ return stream;
+}
+
+//-------------------------------------------------------------------------------------------------
\ No newline at end of file
diff --git a/sgi2018/src/follower/transform.h b/sgi2018/src/follower/transform.h
new file mode 100644
index 0000000000000000000000000000000000000000..bd3909873dcf08de59ec8fc118df512c71e3db6f
--- /dev/null
+++ b/sgi2018/src/follower/transform.h
@@ -0,0 +1,77 @@
+#pragma once
+
+#include <iostream>
+#include "../types.h"
+#include "point.h"
+#include "follow.h"
+
+namespace Transform
+{
+ // takes a starting point, the indexes of the target eigenvalues in the starting point and a vector of parameters to generate ending points
+ // follows the target from the starting point to each of the ending points, independently
+ // returns a matrix with a row per xi and a column per target
+ ComplexMatrix linearPath(const Point& startPoint, const std::vector<unsigned int>& startIndexes, const ComplexVector& xiVector,
+ const number distanceThreshold = 0.05, const number minstepsize = std::sqrt(3.)*1e-6)
+ {
+ // NOTE:
+ // to generate a point from a parameter i, you can use :
+ ComplexMatrix res(xiVector.size(), startIndexes.size());
+ for(unsigned int i = 0; i < xiVector.size(); i ++){
+ Point endPoint(startPoint.omega, startPoint.size, xiVector[startIndexes[i]]);
+ std::vector<unsigned int> indexesResult = Follow::adaptativStep(startPoint, endPoint, startIndexes, distanceThreshold, minstepsize);
+ ComplexVector v(indexesResult.size());
+ for(unsigned int j = 0; j < indexesResult.size(); j ++){
+ v(j) = endPoint.formatedEigenvalues(indexesResult[j]);
+ }
+ res.row(i) = v;
+ //
+ // to follow several targets from a point to another, you can use :
+ }
+ return res;
+ throw std::logic_error("Function not yet implemented.");
+ }
+
+ // takes a starting point, the indexes of the target eigenvalues in the starting point and a vector of parameters to generate ending points
+ // follows the target from the starting point to each of the ending points, independently
+ // returns a matrix with a row per xi and a column per target
+ // NOTE: this function exports the phase speeds of all the eigenvalues to a csv file for later analysis
+ ComplexMatrix linearPath(const Point& startPoint, const std::vector<unsigned int>& startIndexes, const ComplexVector& xiVector,
+ Csv& outCsv, const number distanceThreshold = 0.05, const number minstepsize = std::sqrt(3.)*1e-6)
+ {
+ // NOTE: identical to the previous function but dumps all eigenvalues produced, not just targets, to outCsv
+ //
+ // to output the eigenvalues of a point, you can use :
+ // ComplexMatrix res(xiVector.size(), startIndexes.size());
+ // outCsv.write( (ComplexVector) phaseSpeed(startPoint.omega, startPoint.formatedEigenvalues) );
+ // for(unsigned int i = 0; i < xiVector.size(); i ++){
+ // Point endPoint(startPoint.omega, startPoint.size, xiVector[i]);
+ // outCsv.write( (ComplexVector) phaseSpeed(startPoint.omega, point.formatedEigenvalues) );
+ // //
+ // // to follow several targets from a point to another, you can use :
+ // if(i in startIndexes){
+ // std::vector<unsigned int> indexesResult = Follow::adaptativStep(startPoint, endPoint, startIndexes, distanceThreshold, minstepsize);
+ // res.col(i) = indexesResult;
+ // }
+ // }
+ // return res;
+
+ //
+ // WARNING: you will need some sort of locking mechanism to export values while running in parallel
+ throw std::logic_error("Function not yet implemented.");
+ }
+
+ // takes a starting point, the indexes of the target eigenvalues in the starting point and a vector of parameters to generate ending points
+ // returns a matrix with a row per xi and a column per target
+ //
+ // to do so, this function builds a minimum spanning tree that is processed inparallel
+ // the tree has xi=(0,0) as its root (the starting point) and goes to all the values inside xiVector
+ ComplexMatrix treePath(const Point& startPoint, const std::vector<unsigned int>& startIndexes, const ComplexVector& xiVector, Csv& outCsv,
+ const number distanceThreshold = 0.05, const number minstepsize = std::sqrt(3.)*1e-6)
+ {
+ // FACULTATIV
+ // NOTE: this function can be tricky to implement without using too much memory for large number of points or having an n² complexity
+ // you might want to play with building the tree before processing it or processing it as you are building it
+ // the fastest implementation gets a bonus
+ throw std::logic_error("Function not yet implemented.");
+ }
+}
diff --git a/sgi2018/src/generator.h b/sgi2018/src/generator.h
new file mode 100644
index 0000000000000000000000000000000000000000..3a06cabd4b463e4b0342d1d88e5f4497d939119b
--- /dev/null
+++ b/sgi2018/src/generator.h
@@ -0,0 +1,224 @@
+#pragma once
+
+#include "types.h"
+#include "tools/matlab.h"
+
+
+//-------------------------------------------------------------------------------------------------
+// Constants
+
+namespace Generator
+{
+ // by default, do not use constant continuation
+ bool use_constant_continuation = false;
+}
+
+//-------------------------------------------------------------------------------------------------
+// INTERMEDIATE FUNCTIONS
+
+/*
+ * The function DM = chebdif(N,M) computes the differentiation
+ * matrices D1, D2, ..., DM on Chebyshev nodes.
+ *
+ * Input:
+ * N: Size of differentiation matrix.
+ * M: Number of derivatives required (integer).
+ * Note: 0 < M <= N-1.
+ *
+ * Output:
+ * DM: DM(1:N,1:N,ell) contains ell-th derivative matrix, ell=1..M.
+ *
+ * The code implements two strategies for enhanced
+ * accuracy suggested by W. Don and S. Solomonoff in
+ * SIAM J. Sci. Comp. Vol. 6, pp. 1253--1268 (1994).
+ * The two strategies are (a) the use of trigonometric
+ * identities to avoid the computation of differences
+ * x(k)-x(j) and (b) the use of the "flipping trick"
+ * which is necessary since sin t can be computed to high
+ * relative precision when t is small whereas sin (pi-t) cannot.
+ * J.A.C. Weideman, S.C. Reddy 1998.
+ */
+std::pair<Vector, Matrix> chebdif(const int N)
+{
+ // Indice used for flipping trick.
+ int n2 = (N + 1)/2; // ceil(N/2)
+
+ // Compute theta vector.
+ Vector k = make_vector(0,N-1);
+ Vector th = k*pi/number(N-1);
+
+ // Compute Chebyshev points.
+ Vector x = make_vector(N-1,1-N,-2).unaryExpr([N](number x){return STD::sin( pi*x / number(2*(N-1))) ;});
+
+ Matrix T = repmat(th/number(2.),N);
+ Matrix DX = (T.transpose()+T).binaryExpr(T.transpose()-T, [](number Tplus, number Tminus){return 2. * STD::sin(Tplus) * STD::sin(Tminus);}); // Trigonometric identity.
+ DX.bottomRows(n2) = -flip(DX.topRows(n2));
+ DX.diagonal().array() = 1; // Put 1's on the main diagonal of DX.
+
+ // C is the matrix with entries c(k)/c(j)
+ Matrix C = toeplitz( k.unaryExpr([](number k){return STD::pow(-1,k);}) );
+ C.row(0) *= 2;
+ C.row(N-1) *= 2;
+ C.col(0) /= 2;
+ C.col(N-1) /= 2;
+
+ // Z contains entries 1/(x(k)-x(j)) with zeros on the diagonal.
+ Matrix Z = DX.cwiseInverse();
+ Z.diagonal().array() = 0;
+
+ // D contains diff. matrices.
+ Matrix D = Matrix::Identity(N,N);
+ D = Z.cwiseProduct(C.cwiseProduct(repmat(D.diagonal(),N)) - D); // Off-diagonals
+ D.diagonal() = - D.rowwise().sum(); // Correct main diagonal of D
+
+ return std::make_pair(x, D);
+}
+
+// Compute the sound speed profile
+Vector sound_speed(Vector& z_prof, const complexNumber& xi, const bool use_constant_continuation)
+{
+ // Parameters
+ const auto size = z_prof.size();
+ const number Zstag = 0.2;
+ const number Beta = 1;
+ const number Vref = 2;
+ const number EpsBD = 10;
+ const number Zref = 2;
+ const number a = 1 + 0.2*xi.real(); //+0.2*perturbation.points(indGWS,1);
+ const number Zj = 250; //+20*perturbation.points(indGWS,3);
+ const number Wj = 66.7 + 10*xi.imag(); //+10*perturbation.points(indGWS,2);
+
+ // Bussinger-Dyer
+ Vector UBD = Vector::Zero(size);
+ for(int IndZlocm = 0; IndZlocm < size; IndZlocm++)
+ {
+ if(z_prof(IndZlocm) > Zstag)
+ {
+ UBD(IndZlocm) = STD::log(z_prof(IndZlocm)/Zstag) + Beta*(z_prof(IndZlocm)-Zstag);
+ }
+ }
+
+ // Jet
+ Vector UJET;
+ if (use_constant_continuation)
+ {
+ // Jet with constant continuation to avoid tunnel effect
+ UJET = Vector::Ones(size);
+ for(unsigned int IndZlocm = 0; IndZlocm < size; IndZlocm++)
+ {
+ if(z_prof(IndZlocm) < Zj)
+ {
+ UJET(IndZlocm) = STD::exp(-squared((z_prof(IndZlocm)-Zj)/Wj));
+ }
+ }
+ }
+ else
+ {
+ // Jet without constant continuation
+ UJET = z_prof.unaryExpr([Zj,Wj](number z_prof){return STD::exp(-squared((z_prof-Zj)/Wj));});
+ }
+
+ // Wind profile
+ number UBD_ref = STD::log(Zref/Zstag) + Beta*(Zref-Zstag);
+ Vector Ulocm = UBD.binaryExpr(UJET, [Vref,EpsBD,UBD_ref,a](number UBD, number UJET){return Vref*(EpsBD+UBD_ref)/UBD_ref*(UBD/(EpsBD+UBD)+a*UJET);});
+
+ // Temperature profile
+ const number TG = 290;
+ const number Delta = 10;
+ const number Alpha = 0.03;
+ const number Gamma = 0; //0.01;
+
+ Vector Tlocm = z_prof.unaryExpr([TG,Delta,Alpha,Gamma](number z_prof){return TG + Delta*(1.-STD::exp(-Alpha*z_prof)) - Gamma*z_prof;});
+
+ // Sound Speed profile
+ Vector Clocm = Tlocm.binaryExpr(Ulocm, [](number Tlocm, number Ulocm){return STD::sqrt(1.4*287*Tlocm) + Ulocm;});
+
+ return Clocm;
+}
+
+//-------------------------------------------------------------------------------------------------
+// OPERATOR DEFINITION
+
+ComplexMatrix matrixEDO(const int N, const complexNumber& omega, const complexNumber& xi, const number k, const bool use_constant_continuation)
+{
+ Vector x;
+ Matrix D;
+ std::tie(x, D) = chebdif(N);
+
+ const number zmax = 1e3;
+ Vector Z = x.unaryExpr([zmax](number x){return zmax*(1.-x)/2.;});
+
+ Matrix A = Matrix::Identity(N,N);
+ number B = 0;
+ ComplexVector C = sound_speed(Z, xi, use_constant_continuation).unaryExpr([omega,k](number sz){return squared(omega) / squared(sz) - squared(k);});
+
+ D = -2/zmax*D;
+ Matrix DD = D*D;
+
+ ComplexMatrix M = A*DD + B*D;
+ M.diagonal() += C;
+
+ // Boundary conditions
+ const number a1 = 0;
+ const number b1 = 1;
+ const number c1 = 0;
+ const number aN = 0;
+ const number bN = 0;
+ const number cN = 1;
+
+ M.row(0) = a1*DD.row(0) + b1*D.row(0);
+ M(0,0) += c1;
+ M.row(N-1) = aN*DD.row(N-1) + bN*D.row(N-1);
+ M(N-1,N-1) += cN;
+
+ return M;
+}
+
+/*
+ * Compute the discretization of the operator M=operator(omega,N)
+ * -omega : freq. at which the computation is done
+ * /!\ omega can have an imaginary part
+ * - N : vertical discretization
+ * - M : discretized operator using spectral collocation
+ */
+ComplexMatrix generator(const complexNumber omega, const int N, const complexNumber xi = complexNumber(0.,0.), const bool use_constant_continuation = Generator::use_constant_continuation)
+{
+ ComplexMatrix M0 = matrixEDO(N, omega, xi, 0, use_constant_continuation);
+
+ //ComplexMatrix M1 = matrixEDO(N, omega, xi_a, xi_Wj, 1, use_constant_continuation);
+ //ComplexMatrix M = mldivide(M0, M0 - M1);
+
+ // note that M0 - M1 is ID for all values except its first and last lines
+ // which are (a1*DD.row(0) + b1*D.row(0)) and (aN*DD.row(N-1) + bN*D.row(N-1))
+ // those are 0 for the current boundary conditions
+ // meaning that we are basically computing M0^-1 with two zero columns on the sides
+ // hence the following method gives the expected matrix but quicker and with improved precision
+ ComplexMatrix M = M0.inverse();
+ M.col(0).array() = complexNumber(0.,0.);
+ M.col(N-1).array() = complexNumber(0.,0.);
+
+ return M;
+}
+
+//-------------------------------------------------------------------------------------------------
+// EIGENVALUE TRANSFORMATION
+
+// put an eigenvalue in the proper output space
+complexNumber transformEigenvalue(const complexNumber eigenvalue)
+{
+ return number(1.) / std::sqrt(eigenvalue);
+}
+
+// take an eigenvalue, omega and compute its phase speed
+complexNumber phaseSpeed(const number omega, const complexNumber eigenvalue)
+{
+ return complexNumber(omega / eigenvalue.real(), eigenvalue.imag());
+}
+
+// take a matrix of eigenvalues, omega and compute their phase speed
+ComplexMatrix phaseSpeed(const number omega, const ComplexMatrix& eigenvalues)
+{
+ return eigenvalues.unaryExpr([omega](const complexNumber e){return phaseSpeed(omega, e) ;});
+}
+
+//-------------------------------------------------------------------------------------------------
\ No newline at end of file
diff --git a/sgi2018/src/main.cpp b/sgi2018/src/main.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..ab72b85d8d69f63716b0a61a4ca45f9e4f91a9a0
--- /dev/null
+++ b/sgi2018/src/main.cpp
@@ -0,0 +1,91 @@
+
+#include <iostream>
+#include "types.h"
+#include "tools/csv.h"
+#include "follower/point.h"
+#include "follower/transform.h"
+
+//-------------------------------------------------------------------------------------------------
+// TARGETS
+
+// formated eigenvalues of interest for omega = 10Hz
+auto formatedTargetEigenvalues_10Hz = []()
+{
+ std::vector<complexNumber> formatedTargetEigenvalues_10Hz =
+ {
+ complexNumber(0.35561, 2.8487e-05),
+ complexNumber(0.354, 2.848e-05),
+ };
+
+ return formatedTargetEigenvalues_10Hz;
+};
+
+// formated eigenvalues of interest for omega = 20Hz
+auto formatedTargetEigenvalues_20Hz = []()
+{
+ std::vector<complexNumber> formatedTargetEigenvalues_20Hz;
+ if(Generator::use_constant_continuation)
+ {
+ formatedTargetEigenvalues_20Hz =
+ {
+ complexNumber(3.6103700000000000e-01, 2.8933800000000001e-05),
+ complexNumber(3.5561300000000001e-01, 2.8487699999999998e-05),
+ complexNumber(3.5397600000000001e-01, 2.8485500000000000e-05),
+ complexNumber(3.5202299999999997e-01, 2.8547700000000001e-05),
+ complexNumber(3.4986499999999998e-01, 2.8571900000000000e-05),
+ complexNumber(3.4782600000000002e-01, 2.8344600000000000e-05),
+ complexNumber(3.4604499999999999e-01, 2.7885000000000002e-05),
+ complexNumber(3.4399000000000002e-01, 2.8099100000000000e-05),
+ complexNumber(3.4109699999999998e-01, 2.8376100000000001e-05)
+ };
+ }
+ else
+ {
+ formatedTargetEigenvalues_20Hz =
+ {
+ complexNumber(0.361033647187131, 0.000028933251563),
+ complexNumber(0.355614091880504, 0.000028486937552),
+ complexNumber(0.353997839239009, 0.000028480251433),
+ complexNumber(0.352101292441200, 0.000028478101360),
+ complexNumber(0.348275599694248, 0.000028517568097),
+ complexNumber(0.352097123839055, 0.000028504433229),
+ complexNumber(0.352629811458154, 0.000028414037120),
+ complexNumber(0.353112905615286, 0.000028382664958),
+ complexNumber(0.353546771365575, 0.000028353869735)
+ };
+ }
+
+ return formatedTargetEigenvalues_20Hz;
+};
+
+//-------------------------------------------------------------------------------------------------
+// MAIN
+
+int main(int argc, char *argv[])
+{
+ std::cout << "Starting..." << std::endl;
+ const number omega = 20*2*pi; // 20Hz
+ const int N_gPC = 1000;
+ const unsigned int size = (argc > 1) ? atoi(argv[1]) : 50;
+ const std::string outPutfolder = Csv::confirmedFolder("output/");
+ Generator::use_constant_continuation = true; // makes eigenvalues easier to follow ?
+
+ std::cout << "Defining target eigenvalues... (omega=" << omega << ')' << std::endl;
+
+ const Point startingPoint(omega, size);
+ const std::vector<complexNumber> targetformatedEigenValues = formatedTargetEigenvalues_20Hz();
+ const std::vector<unsigned int> indexTargets = startingPoint.findClosest(targetformatedEigenValues).first;
+
+ std::cout << "Generating " << N_gPC << " random points..." << std::endl;
+
+ const ComplexVector xiVector = randn(N_gPC);
+ Csv::write(outPutfolder + "xi.csv", xiVector);
+
+ std::cout << "MONTE-CARLO: Following target with raw computation..." << std::endl;
+
+ Csv allEigenvaluesCsv(outPutfolder + "phase_eigenvalues.csv"); // to dump the phases of all the eigenvalues we meet
+ const ComplexMatrix eigenvaluesMC = Transform::linearPath(startingPoint, indexTargets, xiVector, allEigenvaluesCsv);
+ Csv::write(outPutfolder + "phase_montecarlo.csv", phaseSpeed(omega, eigenvaluesMC));
+
+ return 0;
+}
diff --git a/sgi2018/src/tools/csv.h b/sgi2018/src/tools/csv.h
new file mode 100644
index 0000000000000000000000000000000000000000..fc29605580dd3a136ecc4106de8aa69f9debb55e
--- /dev/null
+++ b/sgi2018/src/tools/csv.h
@@ -0,0 +1,98 @@
+#pragma once
+
+#include <iostream>
+#include <fstream>
+#include <sys/types.h>
+#include <sys/stat.h>
+#include <exception>
+#include "../types.h"
+
+/*
+ * encapsulate writing to a csv file
+ */
+class Csv
+{
+private:
+ std::ofstream file;
+
+public:
+ explicit Csv(const std::string& filename): file(filename) {};
+
+ // writes a single number to the file
+ template<typename N> void write(const N& x, const char separator = ',')
+ {
+ file << x << separator;
+ };
+
+ // writes a shaman number to the file, splitting result and error
+ #ifdef SHAMAN
+ template<typename NumberType, typename ErrorType, typename PreciseType>
+ void write(const S<NumberType,ErrorType,PreciseType>& x, const char separator = ',')
+ {
+ file << x.number << separator << std::abs(x.error) << separator;
+ };
+ #endif
+
+ // writes a single complex number to the file
+ void write(const complexNumber& x, const char separator = ',')
+ {
+ write(x.real());
+ write(x.imag());
+ file << '\t';
+ };
+
+ // write a full line, separated by the given separator, to the csv
+ void write(const ComplexVector& values, const char separator = ',')
+ {
+ for(unsigned int i = 0; i < values.size(); i++)
+ {
+ write(values[i]);
+ }
+
+ file << '\n';
+ };
+
+ //---------------------------------------------------------------------------------------------
+ // STATIC
+
+ // throws an exception if a folder does not exist, otherwise return the path to the folder
+ static std::string confirmedFolder(std::string folderPath)
+ {
+ struct stat info;
+ if(stat(folderPath.c_str(), &info ) != 0)
+ {
+ throw std::invalid_argument("The folder '" + folderPath + "' does not exist!");
+ }
+ else
+ {
+ return folderPath;
+ }
+ }
+
+ // writes a matrix to a file
+ static void write(const std::string& filename, const ComplexMatrix& matrix, const char separator = ',')
+ {
+ std::ofstream file(filename);
+
+ for(unsigned int r=0; r < matrix.rows(); r++)
+ {
+ for (unsigned int c=0; c < matrix.cols(); c++)
+ {
+ complexNumber x = matrix(r,c);
+
+ #ifdef SHAMAN
+ file << x.real().number << separator << std::abs(x.real().error) << separator
+ << x.imag().number << separator << std::abs(x.imag().error);
+ #else
+ file << x.real() << separator << x.imag();
+ #endif
+
+ if(c+1 < matrix.cols())
+ {
+ file << separator;
+ }
+ }
+ file << '\n';
+ }
+ }
+};
diff --git a/sgi2018/src/tools/matlab.h b/sgi2018/src/tools/matlab.h
new file mode 100644
index 0000000000000000000000000000000000000000..1bc93c3d4082c6d64ab4e11873503d6a6c2de113
--- /dev/null
+++ b/sgi2018/src/tools/matlab.h
@@ -0,0 +1,187 @@
+#pragma once
+
+#include <random>
+#include <iostream>
+#include <fstream>
+#include "../types.h"
+
+/*
+ * Code translated from Matlab base functions
+ * matlab translation guide : https://eigen.tuxfamily.org/dox/AsciiQuickReference.txt
+ */
+
+//-------------------------------------------------------------------------------------------------
+// VARIOUS
+
+const number pi = M_PI;
+
+// squares a number
+template<typename T> inline T squared(const T& x)
+{
+ return x*x;
+}
+
+//-------------------------------------------------------------------------------------------------
+// ALGEBRA
+
+// build a vector with values in the given interval
+Vector make_vector(const int fromValue, const int toValue, const int by = 1)
+{
+ int size = 1 + (toValue - fromValue) / by;
+ Vector result(size);
+
+ int currentValue = fromValue;
+ for(int i = 0; i < size; i++)
+ {
+ result(i) = currentValue;
+ currentValue += by;
+ }
+
+ return result;
+}
+
+// repeats a column vector n times in order to build a matrix
+Matrix repmat(const Vector& v, const int colNumber)
+{
+ Matrix result(v.size(), colNumber);
+
+ for(int col = 0; col < colNumber; col++)
+ {
+ result.col(col) = v;
+ }
+
+ return result;
+}
+
+// solves m = m1 \ m2
+inline ComplexMatrix mldivide(const ComplexMatrix& m1, const ComplexMatrix& m2)
+{
+ //return m1.colPivHouseholderQr().solve(m2);
+ return m1.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(m2); // you can use JacobiSVD for improved precision
+}
+
+// returns an hermitian matrix where v is the first row and conj(v) the first column
+Matrix toeplitz(const Vector& v)
+{
+ auto size = v.size();
+ Matrix result(size, size);
+
+ for(int row=0; row<size; row++)
+ {
+ for(int col=0; col<size; col++)
+ {
+ // complex
+ /*number value = v(std::abs(row - col));
+ if(row > col)
+ {
+ value = Sstd::conj(value);
+ }
+ result(row,col) = value;*/
+
+ // real
+ result(row,col) = v(std::abs(row - col));
+ }
+ }
+
+ return result;
+}
+
+// flip the column and rows
+inline Matrix flip(Matrix mat)
+{
+ Matrix matflipr = mat.rowwise().reverse(); // fliplr
+ Matrix matflipc = matflipr.colwise().reverse(); // flipud
+ return matflipc;
+}
+
+//-------------------------------------------------------------------------------------------------
+// POLYNOMIAL
+
+/*
+ * evaluates a polynomial on the given data
+ * use Horner's scheme
+ * NOTE: one could use a more numerically stable algorithm
+ */
+Vector polyval(const Polynomial& pol, const Vector& x)
+{
+ Vector result = Vector::Zero(x.size());
+
+ for(const auto& coef : pol)
+ {
+ result = result.binaryExpr(x, [coef](const number& result, const number& x){return result*x + coef;});
+ }
+
+ return result;
+}
+
+//-------------------------------------------------------------------------------------------------
+// RANDOM
+
+// generate an uniformaly distributed random number sampled from [-1;1]
+inline number randu()
+{
+ throw std::logic_error("Function not yet implemented.");
+}
+
+// generates a vector of the given size, the entries of the vector are all complex number
+// their real and imaginary parts are uniformaly distributed random number sampled from [-1;1]
+ComplexVector randu(int size)
+{
+ // NOTE: this can be built on the previous function
+ throw std::logic_error("Function not yet implemented.");
+}
+
+// generate a normally distributed random number
+// sampled from a distribution with mean 0 and std 1
+inline number randn()
+{
+ throw std::logic_error("Function not yet implemented.");
+}
+
+// generates a vector of the given size, the entries of the vector are all complex number
+// their real and imaginary parts are sampled from a normal distribution with mean 0 and std 1
+ComplexVector randn(int size)
+{
+ // NOTE: this can be built on the previous function
+ throw std::logic_error("Function not yet implemented.");
+}
+
+//-------------------------------------------------------------------------------------------------
+// IMPORT
+
+/// import a vector of reals from a file
+Vector loadRealVector(const std::string& file)
+{
+ std::vector<number> result;
+ std::ifstream input(file);
+
+ number x;
+ while (input >> x)
+ {
+ result.push_back(x);
+ }
+
+ Vector output = Eigen::Map<Vector, Eigen::Unaligned>(result.data(), result.size());
+ return output;
+}
+
+/// import a vector of complex from a file
+ComplexVector loadComplexVector(const std::string& file)
+{
+ std::vector<complexNumber> result;
+ std::ifstream input(file);
+
+ number r;
+ number i;
+ while (input >> r)
+ {
+ input >> i;
+ complexNumber x(r,i);
+ result.push_back(x);
+ }
+
+ ComplexVector output = Eigen::Map<ComplexVector, Eigen::Unaligned>(result.data(), result.size());
+ return output;
+}
+
+//-------------------------------------------------------------------------------------------------
\ No newline at end of file
diff --git a/sgi2018/src/types.h b/sgi2018/src/types.h
new file mode 100644
index 0000000000000000000000000000000000000000..884a9adee62addf3a2de32bc286370e4f5f01a33
--- /dev/null
+++ b/sgi2018/src/types.h
@@ -0,0 +1,40 @@
+#pragma once
+
+#include <complex>
+#include <vector>
+#include <Eigen/Dense>
+
+#ifdef SHAMAN
+
+#include <shaman.h>
+#include <shaman/helpers/Shaman_eigen.h>
+
+// types used in the program
+typedef Sdouble number;
+typedef Sfloat halfNumber;
+typedef std::complex<number> complexNumber;
+typedef Eigen::SVectorXd Vector;
+typedef Eigen::SRowVectorXd RowVector;
+typedef Eigen::SVectorXcd ComplexVector;
+typedef Eigen::SRowVectorXcd RowComplexVector;
+typedef Eigen::SMatrixXd Matrix;
+typedef Eigen::SMatrixXcd ComplexMatrix;
+typedef std::vector<number> Polynomial;
+#define STD Sstd
+
+#else
+
+// types used in the program
+typedef double number;
+typedef float halfNumber;
+typedef std::complex<number> complexNumber;
+typedef Eigen::VectorXd Vector;
+typedef Eigen::RowVectorXd RowVector;
+typedef Eigen::VectorXcd ComplexVector;
+typedef Eigen::RowVectorXcd RowComplexVector;
+typedef Eigen::MatrixXd Matrix;
+typedef Eigen::MatrixXcd ComplexMatrix;
+typedef std::vector<number> Polynomial;
+#define STD std
+
+#endif